YES(?,O(n^1))
1102.80/297.02	YES(?,O(n^1))
1102.80/297.02	
1102.80/297.02	We are left with following problem, upon which TcT provides the
1102.80/297.02	certificate YES(?,O(n^1)).
1102.80/297.02	
1102.80/297.02	Strict Trs:
1102.80/297.02	  { 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1))))))))))
1102.80/297.02	  , 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
1102.80/297.02	  , 0(1(2(1(x1)))) ->
1102.80/297.02	    1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
1102.80/297.02	  , 0(1(2(1(x1)))) ->
1102.80/297.02	    1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
1102.80/297.02	  , 0(1(2(1(x1)))) ->
1102.80/297.02	    1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
1102.80/297.02	  , 0(1(2(1(x1)))) ->
1102.80/297.02	    1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))) }
1102.80/297.02	Obligation:
1102.80/297.02	  derivational complexity
1102.80/297.02	Answer:
1102.80/297.02	  YES(?,O(n^1))
1102.80/297.02	
1102.80/297.02	The problem is match-bounded by 3. The enriched problem is
1102.80/297.02	compatible with the following automaton.
1102.80/297.02	{ 0_0(1) -> 1
1102.80/297.02	, 0_1(6) -> 5
1102.80/297.02	, 0_1(9) -> 8
1102.80/297.02	, 0_2(26) -> 25
1102.80/297.02	, 0_2(29) -> 28
1102.80/297.02	, 0_2(32) -> 31
1102.80/297.02	, 0_2(38) -> 37
1102.80/297.02	, 0_3(50) -> 49
1102.80/297.02	, 0_3(53) -> 52
1102.80/297.02	, 0_3(56) -> 55
1102.80/297.02	, 0_3(59) -> 58
1102.80/297.02	, 0_3(62) -> 61
1102.80/297.02	, 0_3(68) -> 67
1102.80/297.02	, 0_3(71) -> 70
1102.80/297.02	, 0_3(74) -> 73
1102.80/297.02	, 0_3(77) -> 76
1102.80/297.02	, 0_3(80) -> 79
1102.80/297.02	, 0_3(83) -> 82
1102.80/297.02	, 0_3(89) -> 88
1102.80/297.02	, 0_3(92) -> 91
1102.80/297.02	, 0_3(95) -> 94
1102.80/297.02	, 0_3(98) -> 97
1102.80/297.02	, 0_3(101) -> 100
1102.80/297.02	, 0_3(104) -> 103
1102.80/297.02	, 0_3(107) -> 106
1102.80/297.02	, 0_3(113) -> 112
1102.80/297.02	, 0_3(116) -> 115
1102.80/297.02	, 1_0(1) -> 1
1102.80/297.02	, 1_1(2) -> 1
1102.80/297.02	, 1_1(2) -> 8
1102.80/297.02	, 1_1(4) -> 3
1102.80/297.02	, 1_1(5) -> 4
1102.80/297.02	, 1_1(7) -> 6
1102.80/297.02	, 1_1(10) -> 9
1102.80/297.02	, 1_2(22) -> 5
1102.80/297.02	, 1_2(22) -> 8
1102.80/297.02	, 1_2(24) -> 23
1102.80/297.02	, 1_2(25) -> 24
1102.80/297.02	, 1_2(27) -> 26
1102.80/297.02	, 1_2(28) -> 36
1102.80/297.02	, 1_2(30) -> 29
1102.80/297.02	, 1_2(33) -> 32
1102.80/297.02	, 1_2(34) -> 5
1102.80/297.02	, 1_2(34) -> 8
1102.80/297.02	, 1_2(36) -> 35
1102.80/297.02	, 1_2(37) -> 36
1102.80/297.02	, 1_2(39) -> 38
1102.80/297.02	, 1_3(46) -> 31
1102.80/297.02	, 1_3(48) -> 47
1102.80/297.02	, 1_3(49) -> 48
1102.80/297.02	, 1_3(51) -> 50
1102.80/297.02	, 1_3(52) -> 48
1102.80/297.02	, 1_3(54) -> 53
1102.80/297.02	, 1_3(55) -> 48
1102.80/297.02	, 1_3(57) -> 56
1102.80/297.02	, 1_3(58) -> 48
1102.80/297.02	, 1_3(60) -> 59
1102.80/297.02	, 1_3(63) -> 62
1102.80/297.02	, 1_3(64) -> 28
1102.80/297.02	, 1_3(66) -> 65
1102.80/297.02	, 1_3(67) -> 66
1102.80/297.02	, 1_3(69) -> 68
1102.80/297.02	, 1_3(70) -> 66
1102.80/297.02	, 1_3(72) -> 71
1102.80/297.02	, 1_3(73) -> 66
1102.80/297.02	, 1_3(75) -> 74
1102.80/297.02	, 1_3(76) -> 66
1102.80/297.02	, 1_3(78) -> 77
1102.80/297.02	, 1_3(79) -> 66
1102.80/297.02	, 1_3(81) -> 80
1102.80/297.02	, 1_3(84) -> 83
1102.80/297.02	, 1_3(85) -> 25
1102.80/297.02	, 1_3(87) -> 86
1102.80/297.02	, 1_3(88) -> 87
1102.80/297.02	, 1_3(90) -> 89
1102.80/297.02	, 1_3(91) -> 87
1102.80/297.02	, 1_3(93) -> 92
1102.80/297.02	, 1_3(94) -> 87
1102.80/297.02	, 1_3(96) -> 95
1102.80/297.02	, 1_3(97) -> 87
1102.80/297.02	, 1_3(99) -> 98
1102.80/297.02	, 1_3(100) -> 87
1102.80/297.02	, 1_3(102) -> 101
1102.80/297.02	, 1_3(103) -> 87
1102.80/297.02	, 1_3(105) -> 104
1102.80/297.02	, 1_3(108) -> 107
1102.80/297.02	, 1_3(109) -> 37
1102.80/297.02	, 1_3(111) -> 110
1102.80/297.02	, 1_3(112) -> 111
1102.80/297.02	, 1_3(114) -> 113
1102.80/297.02	, 1_3(117) -> 116
1102.80/297.02	, 2_0(1) -> 1
1102.80/297.02	, 2_1(1) -> 10
1102.80/297.02	, 2_1(2) -> 7
1102.80/297.02	, 2_1(3) -> 2
1102.80/297.02	, 2_1(4) -> 7
1102.80/297.02	, 2_1(5) -> 7
1102.80/297.02	, 2_1(8) -> 7
1102.80/297.02	, 2_2(2) -> 33
1102.80/297.02	, 2_2(5) -> 33
1102.80/297.02	, 2_2(22) -> 33
1102.80/297.02	, 2_2(23) -> 22
1102.80/297.02	, 2_2(25) -> 39
1102.80/297.02	, 2_2(28) -> 27
1102.80/297.02	, 2_2(31) -> 30
1102.80/297.02	, 2_2(34) -> 27
1102.80/297.02	, 2_2(35) -> 34
1102.80/297.02	, 2_2(37) -> 39
1102.80/297.02	, 2_3(22) -> 51
1102.80/297.02	, 2_3(34) -> 63
1102.80/297.02	, 2_3(46) -> 84
1102.80/297.02	, 2_3(47) -> 46
1102.80/297.02	, 2_3(49) -> 51
1102.80/297.02	, 2_3(52) -> 51
1102.80/297.02	, 2_3(55) -> 54
1102.80/297.02	, 2_3(58) -> 57
1102.80/297.02	, 2_3(61) -> 60
1102.80/297.02	, 2_3(64) -> 108
1102.80/297.02	, 2_3(65) -> 64
1102.80/297.02	, 2_3(67) -> 69
1102.80/297.02	, 2_3(70) -> 69
1102.80/297.02	, 2_3(73) -> 72
1102.80/297.02	, 2_3(76) -> 75
1102.80/297.02	, 2_3(79) -> 78
1102.80/297.02	, 2_3(82) -> 81
1102.80/297.02	, 2_3(85) -> 117
1102.80/297.02	, 2_3(86) -> 85
1102.80/297.02	, 2_3(91) -> 90
1102.80/297.02	, 2_3(94) -> 93
1102.80/297.02	, 2_3(97) -> 96
1102.80/297.02	, 2_3(100) -> 99
1102.80/297.02	, 2_3(103) -> 102
1102.80/297.02	, 2_3(106) -> 105
1102.80/297.02	, 2_3(109) -> 114
1102.80/297.02	, 2_3(110) -> 109
1102.80/297.02	, 2_3(112) -> 114
1102.80/297.02	, 2_3(115) -> 114 }
1102.80/297.02	
1102.80/297.02	Hurray, we answered YES(?,O(n^1))
1103.23/297.49	EOF